 | Euclides - 1855 - 230 pages
...parallelogram CF ; ex cequali, K is to M, as the parallelogram AC is to the parallelogram CF (/). But K has to M the ratio which is compounded of the ratios of the sides ; therefore also Ihe parallelogram, AC has to the parallelogram, CF the ratio which is compounded of the ratios of the... | |
 | Euclides - 1855 - 270 pages
...Wherefore, ex cequali, K is to M, as the parallelogram AC is to the parallelogram CF (V. 22). But K has to M the ratio which is compounded of the ratios of the sides, fherefore also the parallelogram AC has to the parallelogram CF, the ratio which is compounded of the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...have the proportion ABCD : AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEORSM. Any two rectangles are to each other as the products of their bases by their altitudes. Let ABCD, AEGF be two rectangles ; the ratio of the rectangle ABCD to the rectangle... | |
 | Euclid - 1859 - 150 pages
...Wherefore, by equality, K is to M as the parallelogram AC is to the parallelogram CF (V. 22). But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. "Wherefore, equiangular parallelograms, &c. QED PROPOSITION XXIV.— THEOREM. ITpóraffiç KÍ'. —... | |
 | Euclides - 1860 - 288 pages
...the parallelogram CF ; K is to M as the parallelogram AC to the parallelogram CP (V. 22); but K has to M the ratio which is compounded of the ratios of...which is compounded of the ratios of the sides. : COR. 1. — If the terms of two analogies are lines, the rectangles ,.i •.• under their corresponding... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...parallelogram CF; ex squali, .TT is to M. as the parallelogram AC to the parallelogram CF: (v. 22.) but K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore, equiangular parallelograms, &c. QED PEOPOS1TION XXTV. THEOREM. Parallclo<jr<tms about the... | |
 | Eucleides - 1860 - 396 pages
...parallelogram CF ; ex aquali, K is to M, as the parallelogram AC is to the parallelogram CF (/). But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. ELM (/) V. 22. COROLLARY 1. If triangles have an angle of the one equal to an angle of the other, they... | |
 | Euclides - 1863 - 122 pages
...Wherefore, ex cequali, K is to M as the parallelogram AC is to the parallelogram CF (V. 22). But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore, equiangular parallelograms, &c. QED C Gin a straight line; and DC and CE shall also be in... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...equal to AE : hence, ABCD : AEFD : : AB : AE ; which was to be proved. 98 PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases and altitudes. Let AB CD and AEGF be two rectangles : then will ABCD be to AEGF, as AB x AD is to AE... | |
 | Euclides - 1864 - 448 pages
...CF; ex tequali, K is to M, as the parallelogram ^Cto the parallelogram CF: (v. 22.) but K has to Jf the ratio which is compounded of the ratios of the...ratio which is compounded of the ratios of the sides. Wherefore, equiangular parallelograms, &c. QED PROPOSITION XXIV. THEOREM. Parallelograms about the... | |
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K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... 
